Symmetry Group Analysis of a Fifth-Order KdV Equation with Variable Coefficients

ABSTRACT

Symmetry group analysis is carried out on a generalized fifth-order KdV (foKdV) equation involving many arbitrary functions. Equivalence transformations group has been determined. This allows us to perform a comprehensive study by reducing the equation to a subclass with fewer number of arbitrary elements. Furthermore, we have established the subclasses of the reduced equation which are nonlinearly self-adjoint. The property of nonlinearly self-adjointness is used to construct conserved vectors from the classical symmetries of the equation by using a general theorem on conservation laws. We also determine conservation laws by using the multipliers method.

KEYWORDS:

• partial differential equations
• conservation laws
• symmetries
• equivalence transformations

Acknowledgments

We would like to thank the referee for his useful comments and careful reading of the paper.

Additional information

Funding

The authors acknowledge the financial support from Junta de Andalucía group FQM–201, University of Cádiz. The second and third author also acknowledge the support of DGICYT project MTM2009-11875 with the participation of FEDER.